An art teacher is making packages of paintbrushes and plant for his students.
He has 24 brushes and 40 tubes of paint. Each package will have the same number
of brushes and the same number of tubes of paint.
a. What is the greatest number of packages that the art teacher can make using
all the paintbrushes and paint? Show your work.

Answer:

~20.6155

Step-by-step explanation:

To compute distance between two points, we can get the vector from one to the other by subtracting them and then computing the length of the vector.

The length of a vector V is:

[tex]|V| = \sqrt{\sum_{i=1}^n v_i^2}\\[/tex]

The vector is:

(9, -5. 4) - (-10, 3, 4) = (9 + 10, -5 - 3, 4 - 4) = (19, -8, 0)

So the length is:

[tex]\sqrt{19^2 + (-8)^2} = \sqrt{361 + 64} = \sqrt{425} = \sqrt{5\cdot 5\cdot 17} = 5\sqrt{17} \approx 20.6155281281[/tex]

Answer:

5/8

Step-by-step explanation:

1/2=4/8

4/8+1/8=5/8

Answer:

x = 557 to the nearest whole number

Step-by-step explanation:

The triangle is divided into two right triangles

Using the SOH CAH TOA identity

tan theta = opp/adj

tan 29 = (x/2)/502

x/2 = 502 tan 29'

x/2 = 278.26

x = 278.26 * 2

x = 556.52

x = 557 to the nearest whole number

Answer:

4/15

Step-by-step explanation:

Total event: 6+4=10

First draw: 6 white out of 10 marbles  6/10

2nd draw: 4 black out of 9 marbles  4/9

probability of drawing a white marble on the first draw polo buy a black marble on the second: 6/10 x 4/9 = 4/15

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Answer:

y=7

Step-by-step explanation:

x=3

Answer:  $61.50

Step-by-step explanation:

To do this you need to first find 18% of 75 which is 13.5 or $13.50 and then subtract that from the original price being $75 and you get $61.50

HOPE THIS HELPS ^^

Answer:

The answer is 61 dollars and 50 cents. So 61.5.

Answer:

2/4

Step-by-step explanation:

2/4 = 4/8

They both equal 1/2

1.1592.5in

3.2521.91mm

Answer:

48

Step-by-step explanation:

Answer:

Infinite number of solutions.

Step-by-step explanation:

Y=5x+1

-5x+Y=1

substitute value of y in first equation (5x+1) into 2nd equation

-5x+5x+1=1

0+1=1

1=1

since answer equals on both sides of the equatio, the answer is determined to be infinite.

Answer:

AOE = 138, EOD = 48

Step-by-step explanation:

Since AD is the diameter of the circle and goes through the middle

angle AOE + angle EOD  = 180

Solving the equation (x + 138) + ( x+ 48) = 180

We get x = 0.

Answer:

-"My step-dad's punch packs a wallop!"

-"The stars shining in the night sky were luminous."

-"The two diametrically opposed viewpoints of ketchup and mustard have been on war for decades."

Answer:

wallop:

daneil crashed on the floor with a wallop

diametrically:

"I regret to say we're diametrically opposed to your ideas", Jessica said to john

luminous:

i have a luminous clock in my room

Step-by-step explanation:

Answer:

z = - 1

Step-by-step explanation:

Given

- 18 = 9z - 9 ( add 9 to both sides )

- 9 = 9z ( divide both sides by 9 )

- 1 = z

Answer:

10178.7602

Step-by-step explanation:

Volume of cylinder= π·r^2·h = π·9^2·40 ≈ 10178.7602

if 18 is the diameter than 9 would be the radius. to make the formula easier.

Answer:

x = 108 because of supplementary angles

Step-by-step explanation:

Solving for x:

Since x and 72 are supplemenatry angles, they'll equal to 180, so:

x + 72 = 180

x = 180 - 72

x = 108

Answer:

n=3

Step-by-step explanation:

To solve the equation divide both sides by 4.

I'm assuming that you want to find n...

Answer:

A

Step-by-step explanation:

The secant- secant angle is half the difference of the intercepted arcs, then

[tex]\frac{1}{2}[/tex] (20x - 7x - 11) = 40 ( multiply both sides by 2 to clear the fraction )

13x - 11 = 80 ( add 11 to both sides )

13x = 91 ( divide both sides by 13 )

x = 7

Then

arc HD = 20x = 20 × 7 = 140° → A

Answer:

they are integers

Step-by-step explanation:

Answer:

?

Step-by-step explanation:

Answer:

21) x = 0

23) x = 7

Step-by-step explanation:

In a parallelogram, the opposite sides are congruent. Using this fact, we can create equations for both problems.

21)

[tex]2x + 18 = 18[/tex]

Subtract 18.

[tex]2x = 0[/tex]

Divide by 2.

[tex]x = 0[/tex]

23)

[tex]2x - 3 = 11[/tex]

Add 3.

[tex]2x = 14[/tex]

Divide by 2.

[tex]x = 7[/tex]

Answer:

the first one

Step-by-step explanation:

Answer:

x=30

m<G

3(30)-17

73

m<H

x+13

43

Step-by-step explanation:

Answer:

m∠G = 73°

m∠H = 43°

Step-by-step explanation:

Use the exterior angle theorem. The exterior angle theorem states that the exterior angle's measurement will be the sum of the two opposite interior angles. Set the equation:

(3x - 17) + (x + 13) = 116

First, combine like terms by simplifying:

3x + x - 17 + 13 = 116

4x - 4 = 116

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. PEMDAS is the order of operation, and stands for:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

~

First, add 4 to both sides of the equation:

4x - 4 = 116

4x - 4 (+4) = 116 (+4)

4x = 116 + 4

4x = 120

Next, divide 4 from both sides of the equation:

(4x)/4 = (120)/4

x = 120/4

x = 30

Plug in 30 for x for each angle measurement:

m∠G = 3x - 17

m∠G = 3(30)  -17

m∠G = 90 - 17

m∠G = 73°

m∠H = x + 13

m∠H = 30 + 13

m∠H = 43°

Check:

180 - 73 - 43 = 64 (Summation of a triangle's angle).

180 - 64 = 116 (Theorem of line).

Answer:

Surface area = 505cm²

Step-by-step explanation:

Surface area of the triangular prism. = 2B + ph

B is the base area

p is the perimeter of the triangle

h is the height of the triangle

Base area = 1/2 * base * height

Base area = 1/2 * 18 * 40

Base area = 9 * 40

Base area = 360cm²

Perimeter of the triangle = 41 + 41 + 18

Perimeter of the triangle = 100cm

height of the prism = 45cm

Surface area = 360 + 100 + 45

Surface area = 505cm²

Answer: 8

Step-by-step explanation: It's just GCF.  The greatest common factor (GCF) of 8 and 16 is 8 (8 and 16 are both divisible by 8 but not by anything greater) which brings us to our answer.

Answer:

Break it into 2 sections: 18 by 3 and 6 by 20

area = 54 + 120

= 174 (answer is A.)

Step-by-step explanation:

9514 1404 393

Answer:

  A.  174

Step-by-step explanation:

Use your number sense. The area can be no larger than the rectangle that is 20 high and 9 wide. That rectangle's area is ...

  A = LW = (20)(9) = 180

The only answer choice smaller than 180 is ...

  A.  174 . . . . . square units

__

If you want to compute it exactly, you can make note of the size of the empty space at the upper left corner. That space is 20-18 = 2 units high and 9-6 = 3 units wide. Its area is A = LW = (3)(2) = 6 square units. When that empty space is subtracted from the overall rectangle area, the result is ...

  180 square units - 6 square units = 174 square units.